# How can I find the shortest path solution or even begin to finding the most optimal solution to a weld robot sequencing problem? [closed]

Not sure this belongs here, but I thought I'd ask: How should I come to an understanding of an optimal weld sequence for a weld robot that welds a physical item on a revolving carousel (the gray T depicted)?

Ok, so the green points need to be welded in the horizontal position (eight on each side), i.e. 180 and 0/360 position (it is currently in the 270 position). The pink points need to be welded in a 0-15% position in the direction indicated. There is no welding from below, i.e., the downward facing pink arrows need to be welded in a downward orientation, and then flipped to weld the other side. In this depiction there are two sides, downward pink arrows can all be access in the 270 position which it currently is in, upward facing arrows need to be rotated to 90 position. The robot can reach the pink arrows in the back in both these positions. The pink arrows all need what is called a "root pass", and need to cool for at least 10 seconds because they also need a "fillet cover" which if done one after the other too fast can cause imperfections. So all eight pink welds have a root and a cover that need to be staggered by at least 10 seconds. The idea here is to limit the travel on the robot, reduce the number of rotations of the carousel, and reduce the time it takes to weld the whole assembly. The depiction is not to scale, the cylinder with the hangman is the robot in its home position.

So, you can ask questions like if I go from home and start on the left downward pink on robot side and rotate to 360 weld out all the green, then weld the right downward pink on robot side would it be the same if I weld both pink downward robot side then all green, and then move on to upward pink at 90 by that time downward pink will be cool should I rotate back to 270 to cover or should I continue to the other side. I don't know, I'm just trying to formula one this so it's as fast as possible. Any thoughts?

Also, at the end it will rotate back to 270 to flip to the other side to be stripped. That is, the carousel is on a carousel.

I was hoping this was the kind of thing that didn't require dimension and could be reduced to graph or something.

• Welcome to Puzzling! You're right, this does not look like a puzzle, but I'm having a hard time figuring out which site is appropriate for this (interesting) question. I'm not really familiar with sites like Operations Research or Computer Science to make a good recommendation. Oct 17, 2021 at 19:04
• I’m siding with @Glorfindel here; while it’s interesting, it certainly isn’t a puzzle. However, that being said, I believe you’ll need to break this down into questions for physics SE and math SE, then finally another for perhaps computer science if needed. Physics for the specifics for welding and how these points will interact, math for optimization, and computer science if you need to get into finer details. Oct 17, 2021 at 19:40
• There are only so many possibilities, so finding the optimal path by examining every possible order of operations is almost certainly the correct call. This problem looks like a very close relative of the travelling salesman, and there are no "neat" general solutions; a brute force search through all the options is the only way to know for sure.
– Bass
Oct 17, 2021 at 20:14